Low-frequency electromagnetic fields in sea environments are a topic of great importance in naval applications like degaussing, mine detection and surveillance. This report deals with mathematical and numerical models for electromagnetic wave propagation at the air-sea surface interface with electric and magnetic sources and receivers in seawater. These models provide tools for the development and analysis of systems of surveillance and protection in naval defence. The lateral wave at the air/sea surface is a significant phenomenon at low frequency electromagnetic wave propagation in seawater. This wave takes a path that goes straight up to the sea surface from a submerged source in seawater, and then the wave propagates radially in air at speed of light and at the same time it induces waves in the seawater by reradiation. Amplitude decay during the propagation path in air is less than for paths in seawater, which makes it possible to achieve longer propagation distances than for a wave entirely confined in the water volume. It is of great importance to develop computational models which are able to quantify actual amplitudes in realistic sea environments with islands and coast lines. In this work we are particularly interested in finite-difference methods because of their wide applicability. The inclusion of both air and seawater in the computational domain is a challenge because of the presence of vastly different wave speeds in air and seawater, which in turn induces different requirements on resolution in space and time. In this report we review those characteristics of the lateral wave that are relevant for numerical modelling by a finite difference method. Special attention is devoted to the problem of domain truncation in the air space. Our main result is that the height of the air layer that needs to be included in the computational domain must be roughly equal to the triple of the source-receiver offset in order to reproduce the lateral wave with good accuracy.